23 citations · 51 across the 18 of their papers we have counts for
5 papers · 1 filter
Arrangements of homothets of a convex body II
Márton Naszódi, Konrad J. Swanepoel
A family of homothets of an o-symmetric convex body K in d-dimensional Euclidean space is called a Minkowski arrangement if no homothet contains the center of any other homothet in…
Approximating a convex body by a polytope using the epsilon-net theorem
Márton Naszódi
Giving a joint generalization of a result of Brazitikos, Chasapis and Hioni and results of Giannopoulos and Milman, we prove that roughly $\left\lceil \frac{d}{(1-\vartheta)^d}\ln\…
On the Existence of Ordinary Triangles
Radoslav Fulek, Hossein Nassajian Mojarrad, Márton Naszódi +3
Let be a finite point set in the plane. A \emph{-ordinary triangle} in is a subset of consisting of three non-collinear points such that each of the three lines dete…
The Kneser--Poulsen conjecture for special contractions
Károly Bezdek, Márton Naszódi
The Kneser--Poulsen Conjecture states that if the centers of a family of unit balls in is contracted, then the volume of the union (resp., intersection) does no…
Bounding a global red-blue proportion using local conditions
Márton Naszódi, Leonardo Martínez-Sandoval, Shakhar Smorodinsky
We study the following local-to-global phenomenon: Let and be two finite sets of (blue and red) points in the Euclidean plane . Suppose that in each "neighbor…